What about a shrine to Anuiel, Sithis's counter part? Or how about cutting past the middle man and head straight to Padomay, as Sithis is only the soul of Padomay (and Lorkhan/Shezarr/Shor the soul of Sithis)
Also, worshiping Sithis isn't going to do much. Unlike the princes, Sithis isn't a tangible..thing, so to say. Sithis is the ever changing chaos to Anuiel's complete stasis. It would be like worshiping a fundamental law of nature, and expecting something to come out of it, or hoping that law senpai will notice you today.
In the OB version, she only birthed her 5 childen and they became the Black Hand. In Skyrim, it was said she birthed then killed her 5 babies. In Morrowind/Daggerfall, it was a member of the Thieves Guild who murdered the Potentate, and a rank in the Dark Brotherhood. Point being, this assertion is likely false, as there is another story after another in every game that has had the Dark Brotherhood play a joinable role, and probably lends more credence to the idea that the Night Mother (that we know of) is actually Mephala trolling the entire guild. The original one could be anything at this point.
Also, it was Bravil where her statue was, not Anvil.